Experimental Economics: Double auction vs Posted offer

As a short intro, both double auction and posted offer are market institutions (which is basically a specification of the rules of trade in a market). Let us assume that buyers want to buy and sellers want to sell a specific good, for instance, shoes.

In a double auction institution, buyers bid upward for the shoes and sellers bid downward to sell their shoes, and then a trade happens when these meet. For example, I want to buy the shoes for $5, and then a seller wants to sell it for $7. So then I say '$5.50!' The seller might find it too low and go 'Ok, ok, $6.50'. It goes on and on until we agree on a price. The double auction institution is in fact highly efficient, as it yields the maximum efficiency in trade (this is measured as the economic surplus from the trade divided by the total potential surplus. Economic surplus is calculated like this: for buyers, this is the price you pay minus the price you would be willing to pay for it; say I wanted to pay $6.50 for the shoes but I got it for $6.00, then my surplus is $0.50. Similarly, for sellers, this is the price you receive minus the price you were willing to sell it for; say you were willing to sell the shoes for $5.80 but got $6.00 for it, so your surplus is $0.20).

The posted offer institution is as follows: sellers post a price, and then buyers see the price and decide if they want to buy or not. No bargaining, just a posted price. This tends to be less efficient than the double auction, as maybe some sellers would have been willing to sell for $0.50 less (and possibly make a trade), but cannot bid down due to the price being fixed.
A class experiment would confirm this result. It is actually a rather fun* experiment. In fact, if you're planning on having a birthday party, I would recommend this as an icebreaker or a game in the party. Perhaps I really am too much of a scholar.

*according to my individual preferences